Optimal Prediction Under Asymmetric Loss

The authors study the optimal prediction problem under general loss structures and characterize the optimal predictor. The authors compute it numerically in less tractable cases. A key theme is that the conditionally optimal forecast is biased under asymmetric loss and that the conditionally optimal amount of bias is time-varying in general and depends on higher-order conditional moments. Thus, for example, volatility dynamics (e.g., GARCH effects) are relevant for optimal point prediction under asymmetric loss. More generally, even for models with linear conditional-mean structure, the optimal point predictor is in general nonlinear under asymmetric loss, which provides a link with the broader nonlinear time series literature.